Behavioural Processes 40 (1997) 13 – 25

Peck orders and group size in laying hens: ‘futures contracts’ for non-aggression M. Pagel, M.S. Dawkins Department of Zoology, Uni6ersity of Oxford, South Parks Road, Oxford OX1 3PS, UK Received 17 June 1996; received in revised form 20 September 1996; accepted 24 September 1996

Abstract We analyse a simple model of the establishment and maintenance of dominance hierarchies in hens. To be beneficial, dominance relationships require that the probability of meeting the same individual repeatedly is high, otherwise costs of establishing the dominance relation are never recouped. Winners and losers benefit from dominance relationships, not necessarily from changing the rate at which they acquire resources but by avoiding costly contests over them in future encounters. We show that so-called ‘loser effects’, in which animals base their strategies for contesting resources solely upon their past experiences of winning or losing dominance fights and not upon who their opponent is, cannot work — these strategies (‘pragmatists’) must additionally involve either individual or status category recognition. As alternatives to dominance relationships, we show that signals of status or fighting ability that determine access to contested resources are expected to evolve in species with typically large groups because in such conditions the costs of establishing dominance relations are not recouped. Such signals do not depend upon recognizing others individually, but rather upon general category recognition. Status signals are not expected in small groups because dominance relationships are likely to be cheaper and just as effective. The results of the model have implications for the welfare of hens kept in large groups. © 1997 Elsevier Science B.V. Keywords: Aggression; Animal welfare; Dominance; Individual recognition; Peck order; Welfare

1. Introduction Animals of many different species show a marked drop in aggression as they become familiar with a particular small set of other individuals (Chase, 1985). Domestic hens, for example, are highly aggressive to one another when first put together into small groups but gradually form

stable dominance hierarchies or ‘peck orders’ in which aggression levels are much lower (Siegel and Hurst, 1962; Guhl, 1968; Al-Rawi and Craig, 1975; Rushen, 1982). An interesting feature of these dominance hierarchies is that during the initial fights to establish the dyadic dominance relationships, the animals may have no immediate gain. In hens, these initial ‘establishment’ fights

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are costly in the sense that overt damage to the head is common and even the victor gains no resources at the time. The fights are therefore about the future and specifically, about the benefits the animals might receive as a result of establishing their position in the hierarchy before conflicts over resources actually arise (Banks et al., 1979; Lee et al., 1982; Syme et al., 1983; Rushen, 1984). Clutton-Brock and Parker (1995) call fights such as these ‘punishments’ or temporarily spiteful behaviour because benefits both to the animal doing the ‘punishing’ and the ‘victim’ are deferred to the longer term. For there to be any benefit to either participant from fighting over future benefits, however, the results of one fight must be ‘carried over’ in some way to the next or subsequent ones. Precisely how this carry-over effect is achieved can have decisive effects on the type of hierarchy that forms and indeed on whether it forms at all. For example, some hierarchies are reputed to be based upon ‘confidence’ or ‘loser’ effects — that is, each individual bases its decision about whether to fight or retreat in any given interaction simply on its own experience of winning or losing fights (Barnard and Burk, 1979; Chase et al., 1994). In these cases, hierarchy formation would not depend on the probability of meeting the same individuals repeatedly, but rather simply upon the distribution of fight outcomes within the population. On the other hand, if the hierarchy is based on individual recognition and animals avoid fights with those that have beaten them in the past, the probability of encountering the same individual repeatedly becomes critical. We here present a model of repeated interactions between individuals. The model takes into account individual differences in fighting ability, the probability that animals will encounter the same individual on successive occasions, and the concept of settling fights in advance through social dominance. The model makes predictions about how an individual’s optimal behaviour is affected by these factors and also shows that ‘loser’ or ‘confidence’ effects that take no account of who an opponent is are unstable against strategies in which the identity or status of an opponent

is assessed. Our interest is to account for the formation of peck-orders in hens because this kind of dominance hierarchy has been particularly well studied in this species and the degree of aggression in groups of different sizes is an important variable in assessing welfare of hens kept in different husbandry systems (Al-Rawi and Craig, 1975; O’Keefe et al., 1988; Appleby and Hughes, 1991). As we will show, however, the model is also applicable to a much wider range of species and enables us to predict for which other species besides the domestic fowl dominance hierarchies will be advantageous and for which they will not be.

2. The model Hens engage in costly fights to establish and maintain their place in the dominance hierarchy. These fights, which we shall call ‘establishment fights’ take place largely when the peck order is being formed but also when individuals change status. The peck orders that result from a series of establishment fights appear to be based primarily on remembered interactions with other individuals. Recognition and memory of past encounters with specific individuals seem to be involved in determining the behaviour of birds towards one another. For example, hens are known to be able to recognize each other as individuals (Guhl and Ortman, 1953; Bradshaw, 1991), strange individuals receive much higher levels of aggression than familiar ones (Hughes, 1977; Zayan, 1987) and groups of hens that have been together for long enough for a stable peck order to have formed show low levels of aggression. The costs of fighting that hens pay when the peck order is being formed are not the only ones that have to be considered in understanding the kind of interactions that take place within a flock. The actual recognition of another bird, even a familiar one, on subsequent occasions may also have costs. Hens appear to be unable to recognize each other except by going up to another bird and examining or scrutinizing it at a distance of 10–30 cms away (Dawkins, 1995). They show no evidence of being able to discriminate familiar group

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members from unfamiliar birds except when within this distance (Dawkins, 1995) and both familiar and unfamiliar birds are examined in this way. Only after the close-up examination does a difference in behaviour towards familiar and unfamiliar hens become apparent (Dawkins, 1996). These close-up examinations may involve a cost in time to the hen but we will not explicitly model them here, emphasizing instead the presumably more costly physical fights. Following our description of the costs associated with fighting to establish and maintain peckorders, consider the following two strategies. Let, W1 =W0 + N(6j −d)

(1)

denote a hen’s fitness in interactions with another hen, with which it does not have a dyadic dominance relationship, where W0 is some initial fitness, N is the expected number of times the two hens will meet in the future in competition over a resource, 6 is the value of the resource, j is the proportion of times the focal hen gains the resource, and d is the cost of the fight over the resource (‘resource fights’). The term in brackets, therefore, represents the payoff to the focal hen per fight with another hen, and we assume that two hens lacking a dominance relationship always fight when encountering the same resource. Now consider W2 =W0 + N(6k) −c

(2)

which describes a hen’s fitness in interactions with another hen with which it has established a dominance relationship within a peck order, where W0, N and 6, are as in Eq. (1) and k is the proportion of times the hen gains the resource given that a dominance relationship exists and c is the cost of the initial fight to establish the dominance relationship. We assume that c-type costs (establishment fights) can be high, but that they are only paid initially: once a dominance relationship is established, we assume that the hen gets the resource at rate k in all N future encounters and without having to pay the d-type costs. In fact, there may be some skirmishing in the N future encounters, but our assumption is that d-type fights, fights over a resource given that no dominance relationship exists, do not in general occur.

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It will pay a hen to establish a dominance relationship with another hen when W2 \ W1, that is, when cB N(6(k− j )+ d)

(3)

The term on the left of the inequality is the cost of the establishment fight. The term on the right is the difference between the benefits gained in the N future encounters with versus without a dominance relation. Without a dominance relation, resources are acquired at a per encounter rate of (6j− d), whereas with a dominance relation they are acquired at rate (6k). The inequality in Eq. (3) therefore reveals two fundamental features of peck-order formation. One is that the benefits of establishing a dyadic dominance relationship always include the term Nd. This term represents the costs that a hen would have to pay in the N expected future interactions with the individual, were a dominance relationship not established. The term Nd therefore represents expected benefit derived from paying the initial c-type costs of establishing the dominance relationship. The second feature is that the benefit of establishing the relationship is independent of 6, the resource value, if k= j. And, even if k:j, 6 contributes little to the expected benefits. Thus, if dominance relationships do not dramatically alter the rate at which one acquires the resource, then they are established principally to avoid d-type costs in the form of future resource fights. This means that hens might establish dominance hierarchies even without there being a noticeable change in the per encounter rate at which resources are acquired. One scenario in which j and k will tend to be equal is if in any given dyad they both tend either towards 0 or 1 (that is, a given individual tends always to win or lose against another). On the other hand, if for example, j is nearer to 1/2 and k changes either to 0 or to 1 depending upon the outcome of the dominance fight, then the value of the resource can be important. With these considerations in mind, we can say that hens facing the decision of whether or not to establish dominance relationships are in the position of someone pondering whether to buy a ‘futures contract’: dominance relations will be es-

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Fig. 1. Plot of benefits =(T/n)(6(k-j )+ d) versus group size, n, for two different values of T: upper curve T = 30, lower T =10. The horizontal line represents the fixed costs c, here taken as c = 1 (Eq. 4). Where the curves lie above the c =1 line, fights to establish dyadic dominance relationships are advantageous. Below the c = 1 line, fights to establish dyadic dominance relationships are advantageous. Below the c= 1 line the costs of fighting are never repaid. Thus, the critical group size at or below which peck orders are never repaid. Thus, the critical group at or below which peck orders are advantageous varies depending upon the parameters T and n. For a given small group size, individuals should be willing to expend up to the curved line to establish a dyadic dominance relationship. Other parameters: 6 = 1; k = j= 1; d = 1/4. Parameter values are arbitrary but the shape of the curves depends only upon n.

tablished when a hen is willing to pay some initial costs c in return for ‘fixing’ her expected rate of return (benefit) at b =(6(k-j ) +d) in her N future encounters with another hen. Importantly, as inequality Eq. (3) shows, both ‘winners’ and ‘losers’ have an interest in making this investment; dominance relations do not merely serve winners.

3. The effect of group size The expected number of future encounters strongly affects the value of the future encounters and so we seek an expression for N in Eq. (3). Let 1/n represent the number of encounters per unit time that the focal hen will have with a given other hen, where n is the size of the group in which the hen resides and we implicitly assume that individuals are ‘evenly mixed’ in the sense that a given hen is no more likely to meet one hen than another. If T is taken to represent the length of time that an individual remains in the group, then N = T/n is the expected number of encounters with a given individual. It will, therefore, pay a hen to establish a dominance relation whenever

cB (T/n)(6(k− j )+ d)= (T/n)b

(4)

where we now use b to denote the expected benefit of the dominance relation, as described above. Inequality Eq. (4) shows that as n grows large, the expected number of future encounters with a given individual rapidly becomes sufficiently small that a hen may never recoup the costs paid to establish a dyadic dominance relationship. In small groups, however, hens can pay and expect to recoup large costs of establishing dominance relations (Fig. 1) and increasingly so as group size diminishes. These relations are shown in Fig. 1 which plots Eq. (4) against n for two different values of T. Whenever the curves given by (T/n)b in Fig. 1 lie above the horizontal line given by c, establishing dyadic dominance hierarchies is favoured, otherwise they are not. Hens’ behaviour, if facultative in nature, is predicted to change qualitatively where the (T/n)b and c lines cross. More generally, Fig. 1 shows that whether a given species forms dominance hierarchies may depend upon its species-typical group size. Finally, because of the much stronger dependency of the (T/n)b term on 1/n, than on T (Fig. 1), it appears

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that peck orders will generally only be cost-effective for a narrow range of group sizes. The model shows that hierarchy formation breaks down at larger group sizes not because animals are unable to recognize all the individuals in their group but because they do not benefit from using recognition in this way. The limit on hierarchy formation is thus not recognition capacity per se but probability of re-encountering the same individual.

4. ‘Pragmatist’ versus the ‘loser effect’ The model described in the previous section shows that the expected number of future encounters with the same individual strongly affects the utility of establishing a dominance relationship with that individual. The dominance relationships which are derived from establishment fights are based upon individual recognition. Some authors have suggested that individual recognition is not required to establish dominance hierarchies based upon establishment fights, and so in this section we explore some simple models of dominance relations that do not employ individual recognition and contrast them to one in which some limited recognition is required. The ‘loser’ (‘winner’ or ‘confidence’) effect (Barnard and Burk, 1979; Chase et al., 1994) has been suggested as an alternative means of maintaining a dominance hierarchy. Parker (1974) suggested that prior experience could contribute to resource holding power and there is now evidence from a wide range of taxa that winning or losing a fight can influence an animal’s behaviour in its next aggressive encounter (e.g. Barnard and Burk, 1979; Beaugrand and Zayan, 1985; Beacham and Newman, 1987; Drummond and Osorno, 1992), although Chase et al. (1994) provide evidence that this effect may hold only within certain time limits. In the pumpkinseed sunfish (Lepomis gibbosus) for example, the ‘winner effect’ lasts only between 15 and 60 min, making it difficult to assess the long-term effects on dominance hierarchy formation (Chase et al., 1994). A further difficulty is that the ‘loser effect’ is often imprecisely formulated. For example, a ‘pure’ loser

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effect might mean that an animal bases its decision about whether to attack solely on its prior experience of winning or losing fights with other individuals and takes no account at all of the size or identity of its present opponent. Alternatively, a less rigorously defined ‘loser effect’could just mean that its own prior experience is one of the factors that affects an animal’s behaviour in its next fight. In order to clarify this distinction and to show that a ‘pure’ loser effect is likely to be unstable, we contrast ‘pure loser,’ where the decision about whether to fight is based solely on past experience, with a strategy we call ‘pragmatist’ (Appleby, 1985) — where the decision about whether to fight is based on a mixture of past experience and recognition of the opponent’s identity. We begin with a simple null-model of a ‘pure loser’ effect in which individuals do not recognize other individuals but do have a ‘self-concept’ of their fighting ability based upon their previous encounters. Individuals randomly choose to fight or not to fight other individuals at a rate determined by their self-concept. The model shows that, seen this way, the ‘loser effect’ as an unconditional strategy based upon past performance (and not upon individual recognition) cannot have higher payoffs than two simpler unconditional strageies ‘always fight’ and ‘never fight’. However, we show that a form of ‘loser effect’ based upon individual recognition or limited recognition of ‘types’ is predicted by Eqs. (1) and (2) of our model. Let m represent an individual’s expectation of winning its next encounter, where m is simply the proportion of previous fights an individual has won and may therefore be continually updated. Winning an encounter brings benefits equal to 1 but at cost a for an overall return of 1 − a. Losing brings no benefit but costs a. Because individuals fail to discriminate among others, we assume that individuals fight with probability p= m in any given encounter and fail to fight with probability (1−p)= (1− m), although this is not required for the model. If the composition of the group does not change rapidly, in the p encounters that an individual chooses to fight, it will win m of those fights on average and lose 1− m. It gains

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nothing when it does not fight. The fitness of the loser-effect strategy is thus, WL = p[m(1− a) −(1 − m)a]+(1 − p)(0),

However, we now assume that because the fights are not chosen at random, m* of the fights are won. The fitness of the ‘pragmatist’ strategist is thus WP = p[m*(1− a)− (1−m*)a]+ (1−p)(0),

=p(m −a) Contrast the loser-effect strategy with the two simpler strategies ‘always fight’ and ‘never fight’: WA =[m(1− a)−(1 −m)a],

= m −a Both the ‘loser-effect’ strategy and ‘always fight’ will have higher payoffs than WN when m\ a; that is when the probability of winning is sufficiently high to exceed the cost of losing. If mB a, then the strategy of ‘never fight’ has the highest payoff. However, WL \WA requires p(m− a)\(m −a), which, because p is a proportion (i.e. varies between 0 and 1) is impossible: the loser-effect strategy of randomly fighting with probability m, based upon past experience, cannot have higher payoff than ‘always fight’ on the one hand or ‘never fight’ on the other. The ‘loser effect’ as a strategy, if based solely upon one’s own past rate of success or failure, does not improve upon two simpler alternative strategies. A simple modification to the ‘loser effect’ shows that its failure as a strategy derives from its lack of use of individual recognition or assessment cues. We can introduce the strategy WP where the ‘P’; stands for ‘pragmatist’ to describe a strategy that chooses not to fight an opponent judged to be superior, otherwise it fights. The judgement can be made either upon individual recognition (and thus of recognition that in past fights the opponent has won) or upon a more general category assessment such as the opponent having larger body size. We assume that WP is identical to WL except that now the decision to fight or not is based upon individual recognition or assessment. We assume that the ‘pragmatist’ strategist chooses to fight p proportion of the time, where for ease of comparison we assume that this proportion is equivalent to that for the ‘loser-effect’.

= p(m*− a). The ‘pragmatist’ will have higher fitness than the ‘loser-effect’ whenever m*\m. Thus, for ‘pragmatist’ to improve on the ‘loser-effect’ merely requires that individual recognition or assessment brings a higher proportion of victories. However, does the ‘pragmatist’ strategy improve upon ‘always fight’ or ‘never fight’? The conditions for ‘pragmatist’ to improve upon ‘never fight’ are simply that m*\ a, the same as those for the ‘loser-effect’. ‘Pragmatist’ improves upon ‘always fight’ if m*\

m−a(1− p) p

from which it can be seen that if p=1, ‘pragmatist’ and ‘always-fight’ are equivalent. For values of pB1, the ‘pragmatist’ strategy can improve upon always fight if m* is sufficiently larger than m. This simple modelling exercise shows that individual recognition and assessment will be favoured elements as part of one’s overall strategy of interacting with others. Strategies lacking such recogniton or assessment would seem to be doomed to have lower fitness. An interesting facet of ‘pragmatist’ as a strategy is that an individual hen may show behaviour like that of the ‘loser-effect’ if it judges that it should rarely or never fight. For such a hen, the value of p*: 0 and m* has to be sufficiently large to make the inequality true. If such a hen cannot achieve a sufficiently high value of m*, it can adopt ‘neverfight’ as a strategy. Alternatively, a hen may adopt a ‘loser-effect’ value of p*= 0 against some hens but p* =1 against others. To allow direct comparison of ‘pragmatist’ to our previous strategies W1 and W2, consider that WP can be expressed as WP = W0 + Nu where u is the per encounter payoff to ‘pragmatist’. The value of u would be zero if none of these encounters ever led to getting the resource 6, or it

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Fig. 2. Plot of benefits of establishing a dyadic dominance relation = (6k-nc/T) versus group size, n, for two different values of k, the expected probability of winning future contests over resources, 6: top curve, k =3/4; bottom curve, k =1/4 (Eq. 5). Whenever the dashed lines are above the horizontal u=1/4 line, fights to establish dyadic dominance relations are preferable to a ‘pragmatist’ strategy of not fighting, below the line they are not and a hen playing the ‘pragmatist’ strategy will act like a ‘loser’, i.e. never fight in this circumstance. Where the k =1/4 curve is below the c =1 line but the k =3/4 line is above, two individuals in the same group would have a different optimal strategy depending upon their perceived chance of winning future contests: that is, for these group sizes (and for the parameters chosen), k=1/4 individuals should not fight whereas k = 3/4 individuals should. Equivalently the same focal individual may have differing values of k against different individuals and thus act like a ‘loser’ against some but fight others. Other parameter values: T =5; c= 1; 6= 3.

could be some small positive amount if on some occasions the hen obtained the resource. ‘Pragmatist’ as an alternative to establishing a dyadic dominance relation will be favoured when WP \ W2 or when



u\ 6k−



na . T

(5)

If, for example, a hen assumes that k =0 against some other hen, keeping her head down from the start may be the best strategy against that hen. ‘Pragmatist’ can also be superior to not establishing any sort of dominance relationship (i.e. superior to fighting over the resource at each new encounter) if WP \W1, which occurs when u\ (6j− d).

(6)

Here again, if j is small enough it may be better for ‘pragmatist’ to surrender than to risk resource fights in future encounters. In either case, it is apparent that a ‘loser effect’ type behaviour can arise if a given hen’s j or k are sufficiently small

for some dyads to make ‘pragmatist’ the best strategy in those cases. This apparent ‘loser effect’ (in reality ‘pragmatist’) is plotted in Fig. 2 and works because the hen recognizes that its success varies from one individual to the next. Fig. 2 shows how different individuals in the same group might adopt different strategies, one playing pragmatist, the other not. Equivalently the figure can correspond to the same individual having different optimal strategies against different opponents, playing pragmatist against one, but not against the other. If the pragmatist model is a relevant description of behaviour, we should not expect that real animals would adopt the pure loser effect but might show ‘pragmatist’ (to particular individuals, possibly including their entire group) or, if individuals were not recognized, use additional information based on assessment of size or strength. The various studies that have demonstrated that prior experience is important in determining fight outcome do not rule out an additional effects of

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individual recognition or assessment (e.g. Beaugrand and Zayan, 1985; Beacham and Newman, 1987; Beaugrand et al., 1991; Drummond and Osorno, 1992). Indeed, prior experience seems to be used only when size differences between opponents are small. When size superiority is considerable, the effect of prior experience disappears and larger animals are aggressive even when their previous fights have resulted in defeat. This suggests that the animals are not playing a ‘pure loser’ strategy. Furthermore, Drummond and Osorno (1992) showed that although second-hatched (and therefore smaller) chicks of the blue-footed booby (Sula nebouxii ) remain subordinate to their siblings throughout the nestling period and transfer their subordinate behaviour to encounters with unfamiliar chicks, they may become more aggressive if they detect a relative size and/or strength advantage. Although behaving somewhat like ‘losers’ they are thus not relying solely on information about their own fighting experience.

5. Group size, behavioural tactics and status signalling We can now ask whether the behaviour predicted by Eq. (4) is the evolutionarily stable as well as optimal strategy. Call the strategy of Eq. (4) ‘optimal-establishment’ and consider the two alternative strategies, which we shall call ‘alwaysestablish’ and ‘never-establish’. From Fig. 1 it can be seen that when n is large never-establish will have the same fitness as optimal-establish but always-establish would have lower fitness. For small n, always-establish and optimal-establish will have the same fitness but never-establish will be lower. If group size fluctuates sufficiently widely, then ‘optimal-establish’ will have higher fitness than the two alternative strategies. This raises the question of whether hens’ behaviour does change facultatively with changes to group size, or whether hens have had a species-typical group size such that one or the other of the simple strategies has been of equal fitness to ‘optimal-establish’. If the latter is true, then because hens evolved from junglefowl in which group size is typically one

male with two–five females (Johnson, 1963), we would expect that hens living in artificially larger groups will inappropriately attempt to establish dominance hierarchies with each of many individuals with whom they will have very little future contact. On the other hand, if hens are able to adjust their behaviour according to the size of group in which they find themselves, we should expect them to abdandon all attempts to establish peck orders and make no attempt to distinguish familiar from unfamiliar individuals at large group sizes. Note that this is not because of an inability to remember the identity of more than a given number of birds, as previously suggested (e.g. McBride and Foenander, 1962; Grigor et al., 1995) but because it will simply not be worth paying the cost of establishing any relationships with birds that are unlikely to be encountered again. Such evidence as exists suggests that with the very large so called ‘flock’ sizes found in the commercial broiler and egg industries (where hundreds or even thousands of birds may be kept together), birds are effectively surrounded by strangers with which they do not establish relationships (Preston and Murphy, 1989) but this point deserves further investigation. If establishing individual pairwise dominance hierarchies does not pay in large groups, what is the optimal strategy? Even though a bird may not often encounter the same individual in a contest over a resource, encounters per se will be frequent and in each one a d-type cost (resource fight) must be paid failing any other convention for settling resource fights. One possibility is that large groups will spontaneously form smaller groups or cliques in which clique-specific peck orders arise. In hens, there is some evidence that this does occur (McBride, 1964; McBride and Foenander, 1962) but the evidence is somewhat contradictory (Hughes et al., 1974; Appleby et al., 1989; Preston and Murphy, 1989). The ‘confidence’ or ‘loser effect’ (Barnard and Burk, 1979; Chase, 1985) suggests another way to avoid dtype costs, but we have shown that as a strategy not based upon individual recognition, it does not work. However, we have shown how a strategy we call ‘pragmatist’ can yield ‘loser effect’ type

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behaviour when some individuals have low rates of success against some other individuals. An alternative that avoids the problem that the costs associated with establishing dominance relations with specific individuals in large groups may not be recouped, is to signal status or fighting ability, for example using ‘badges of status’ (e.g. Rowher, 1975; Maynard Smith and Harper, 1988). Whereas our previous discussion has compared strategies that could change in real time, we now entertain an evolutionary point of view to ask when will a status signalling system be advantageous where a dominance hierarchy is not? Let s be the cost to a signaller of producing, maintaining and displaying a signal of fighting ability. If the signal is a costly ornament, then production and/or maintenance costs will be high. If the signal is a badge of status, production and maintenance costs may be small, but the occasional costs associated with enforcing the message of the badge (probing or being probed) may be high. In either case, we assume that the signal settles disputes over resources. Having such a signal will therefore be advantageous when its cost is less than the sum of the costs of the establishment fights with the n members of the group, that is, when



s B % c−



Tb , n

where the terms are as defined in Eq. (4), and the summation is over all of the individuals with whom the signaller would otherwise have to form dyadic dominance hierarchies. For simplicity, take this number to be equal to n. If n is small, the ratio Tb/n is relatively large and the term in brackets may become very small. This means that signals are unlikely to evolve when group sizes are small. However, as n becomes large, Eq. (6) converges in the limit on s B Sc and thus signals become much more likely as group size increases. That is, when group sizes are large, costs of establishing relationships with all individuals in the group are so great that they may easily outweigh signal costs. Note, that this explanation does not require any assumptions about cognitive abilities. Signals, then, are expected to be advantageous in approximately those circumstances in

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which establishing a peck-order is not and vice versa. However, an important difference between a dominance hierarchy based upon a signal and one based upon a series of dyadic fights, is that the former does not require individual recognition, but rather recognition of categories. Critical variables determining whether or not social interactions are based on individual recognition will thus be the size and stability of the group. For example, turnstones (Arenaria interpres) have considerable plumage variability which appears to be used for individual recognition, not status signalling, and their flocks have relatively stable membership (Whitfield, 1988). On the other hand, species where large numbers of birds are likely to be encountered over a short time, such as great tits (Parus major), rely more on status signalling, amongst other factors (Wilson, 1992). However, if animals are able to adjust their behaviour facultatively according to the size of group they find themselves in, there may not be clear cut differences between species. Rather, individual recognition may be used when groups are small and status signalling when new individuals are constantly encountered. This may account for the conflicting evidence over whether plumage variation is used in individual recognition or status signalling (Rowher, 1985; Whitfield, 1988; Slotow et al., 1993).

6. Aggression, group size and welfare The search for welfare alternatives to the battery cage has led to the development of systems such as free-range and deep-litter in which laying hens may be kept in large flocks. A critical problem is to evaluate the welfare of birds kept in these very large social groups compared to those in smaller groups and one of the measures of interest is the level of aggression. It will be apparent from the preceding discussion, however, that the relationship between group size and aggression is far from simple. Our model shows that some kinds of aggression (those associated with ‘establishment’ fights) will be more frequent in groups small enough for peck orders based on individual recognition to develop than in larger

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groups. On the other hand, it also shows that other kinds of aggression (‘resource fights’) will be commoner in large groups in which it does not pay to establish peck orders. The reason is that in these larger groups, hens will continually engage in ‘resource fights’, resulting, potentially, in more aggression overall. This may account for the somewhat conflicting evidence that exists for the relationship between group size and aggression in hens (e.g. Guhl and Allee, 1944; Al-Rawi and Craig, 1975; Al-Rawi et al., 1976; Hughes and Wood-Gush, 1977). It also leads to a specific prediction: observations of aggressive behaviour in groups of hens of different sizes should reveal differences in the type and nature of the aggressive acts. There is some limited evidence on this point. Lindberg and Nicol (1996a) have recently shown that aggressive pecks (usually to the head and resulting in avoidance) were more common in small groups of four hens that were either semi-familiar or unfamiliar with each other than than in similar large groups of 44 hens. On the other hand, they found that threats (initiator causes recipient to move away but does not physically attack or follow) were most common in small groups of familiar hens. These findings show that the nature of the hens’ interactions with each other can change markedly with group size and with opportunities for becoming familiar with different individuals. Our models predict that what have been described as aggressive pecks in small unfamiliar groups would be, if more closely examined, of the ‘establishment fight’ variety but that this kind of aggression would not be seen in very large groups.

7. Discussion The utility of a peck order derived from a series of dyadic dominance relationships based upon individual recognition depends upon the extent to which the costs paid in establishing each of the individual dyadic dominance relationships will be directly recouped. Costs are recouped largely because a dyadic dominance relationship allows a hen to avoid the fights over resources that other-

wise would be expected to take place in each of that hen’s future encounters with the other hen in the dyad. The likelihood of encountering the same individual in the future declines sharply as group size increases and thus the model suggests that peck orders will only be found if small groups are the norm. The amount of effort that a hen should be willing to expend to establish a dominance relationship is predicted to increase steeply as group size declines, because the number of future encounters will be large. Surprisingly, dyadic dominance hierarchies can be beneficial even when they do not alter the per encounter rate at which resources are acquired: avoiding the costs of future fights over resources can be sufficient on its own, allowing peck orders to serve losers as well as winners. In species in which individuals habitually live in large groups and have a low probability of encountering the same individuals repeatedly, our model predicts that the benefits of individual dominance relations based on fighting will rarely be obtained and so alternative strategies of avoiding fights over resources may be expected to evolve. We show that systems of status signalling allow animals to avoid the costs of establishing dyadic relationships with every other individual in their group, but at the same time allow them also to avoid fights over resources at every encounter. Here the ‘carry-over’ effect is obtained not through remembering an individual’s strengths and weaknesses but through generalizing from one category member to another that carries the same ‘badge’. Barnard and Burk (1979) argued that there is no fundamental difference between dominance hierarchies based on individual recognition and those based on simple cues such as status badges. However, our analysis shows that systems based upon signals do not require individual recognition and are expected to evolve in circumstances in which systems of individual recognition do not pay. The sense in which these two kinds of system are similar is that in each case, a cost (be it of establishing a dominance relationship or of producing a signal) is recouped by avoiding future fights over resources. The important distinction between the two systems is that one is advanta-

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geous when those future encounters are based upon repeated interactions with a small group of individuals, whereas the other is advantageous when the interactions are with a large group and thus the likelihood of repeated interactions is much lower. The stability of both individual recognition and status signalling systems, however, depends on the competitive ability of individuals remaining constant over a sufficient length of time that past experience can be used as a reliable guide to future performance. Where this is not the case, such as situations in which individuals lose or gain condition, animals may then be forced to pay the costs of assessing each other afresh on each occasion with costly pre-fight signals (e.g. Clutton-Brock and Albon, 1979). Some hierarchies are reputed to be based on ‘confidence’ or ‘loser’ effects in which each individual bases its decision of whether to fight or retreat not upon individual recognition, but upon its own history of winning or losing fights (Barnard and Burk, 1979; Chase et al., 1994). We have shown, however, that a ‘pure’ loser (own past history is the sole determinant of whether to fight or retreat) this strategy does not have higher fitness than two simpler strategies: a strategy of ‘never fight’ has higher fitness than the ‘loser’ strategy for individuals with very low probabilities of winning and ‘always fight’ has higher fitness if the probability of winning is high enough. The important point is that, without individual recognition, it is more advantageous to adopt one or the other of these simple strategies than it is to adopt the pure ‘loser’ strategy. If, on the other hand, there is individual recognition, we show that a strategy of ‘pragmatist’ can evolve in which an individual always behaves submissively against certain other players. This strategy is favoured when the probability of winning against a particular other individual is sufficiently low. For individuals of very low average ability, ‘pragmatist’ may emerge as the best strategy against a large number of members of the group. Our model predicts that to gain maximum benefits animals should change their behaviour facultatively in response to changes in their group size. Whether or not they do may depend upon

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such things as what the species-typical mean and variance of group size have been over evolutionary time. Either way, the model can be applied to issues that may be of importance to understanding some aspects of animal welfare. For example, an issue that is very important for hen welfare is the size of group in which these birds should be kept. Ironically, the much-criticized battery cage, with 4–5 birds/cage, results in a group size much nearer to that found in wild jungle-fowl than that commonly found in commercial deep-litter or free-range flocks, with thousands of birds. Our model makes two predictions about the behaviour of hens in different sized groups. Firstly, it predicts that birds should not attempt to establish peck orders in large groups such as those found in commercial free-range and deep litter and that they should fail to use individual recognition in encounters when the probability of re-encountering the same bird is low. Secondly, it predicts that the nature of fights between birds should change with group size. ‘Establishment fights’ in which not only the fighting ability but also the identity of each individual must be learnt should be characteristic of small groups that are initially unfamiliar with each other. Since familiar hens recognize each other by close-up inspection of the head region (Dawkins, 1995, 1996), establishment fights can be expected to involve opportunities for hens to learn the head characteristics of their flock mates, that is, to involve considerable periods of close-up, binocular fixation. ‘Resource fights’, on the other hand, are predicted to be characteristic of large groups of hens in which do not recognize each other as individuals and so would not be expected to involve inspection of the head region but rather simply to drive the opponent away from a resource. Even if domestic hens do facultatively change their behaviour in response to changes in group size along the lines predicted by our model, it would still be an open question as to whether their welfare would be better served in small groups with the ‘punishment’ of peck order formation or in larger groups without it. Just as some people prefer the anonymity of a city to the intense interaction of a village where everyone knows everyone else, so it is an empirical and

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certainly not straightforward matter as to which group size hens prefer (Hughes, 1977; Dawkins, 1982; Lindberg and Nicol, 1996a,b). And, as preference is only one aspect of welfare (Dawkins, 1990) a further question which has yet to be answered is in which group size their long-term welfare is best served. Looking beyond the domestic hen to other species, the third prediction made by our models is that there should be a shift from dominance hierarchies based on individual recognition to those based on status badges or behaviour with species showing increasing group size. In species that use ‘status badges’, there may even be a shift within one species depending on the group size an individual finds itself in. This prediction can be tested either experimentally or by comparative studies. Finally, we predict that animals should not adopt ‘loser’ or ‘confidence’ strategies based solely on their own experience of winning or losing fights but should also take into account either the individual identity or the assessed fighting ability of any new opponent they encounter. This prediction suggests that detailed analysis of successive encounters with the same or different individuals would show that ‘losers’ are using more than just their own experience in deciding whether to fight in future.

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Peck orders and group size in laying hens: `futures contracts' for non-aggression.

We analyse a simple model of the establishment and maintenance of dominance hierarchies in hens. To be beneficial, dominance relationships require tha...
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